When do you factor quadratic equations

This method is also is called the method of factorization of quadratic equations. Factorization of quadratic equations can be done using different methods such as splitting the middle term, using the quadratic formula, completing the squares, etc.

The factor theorem relates the linear factors and the zeros of any polynomial. They are the zeros of the quadratic equation. Let us go through some examples of factoring quadratics:. Verify by substituting the roots in the given equation and check if the value equals 0. Factoring quadratics gives us the roots of the quadratic equation. There are different methods that can be used for factoring quadratic equations.

Factoring quadratics is done in 4 ways:. Factoring quadratics can be done by finding the common numeric factor and the algebraic factors shared by the terms in the quadratic equation and then take them out. Let us solve an example to understand the factoring quadratic equations by taking the GCD out. We determine the factor pairs of the product of a and c such that their sum is equal to b. Split the middle term 8x in such a way that the factors of the product of 1 and 12 add up to make 8.

Factor pairs of 12 are 1, 12 , 2, 6 , 3, 4. Now, we can see that the factor pair 2, 6 satisfies our purpose as the sum of 6 and 2 is 8 and the product is You can practice simple quadratic factoring. Well, one of the big benefits of factoring is that we can find the roots of the quadratic equation where the equation is zero. We can also try graphing the quadratic equation. Seeing where it equals zero can give us clues. There is also a general solution useful when the above method fails , which uses the quadratic formula :.

A Quadratic Equation in Standard Form a , b , and c can have any value, except that a can't be 0. The Quadratic Formula takes longer and you have to be careful with arithmetic but it will give results when factoring won't work.

The quadratic formula may also demonstrate when no solution exists something that is difficult to see with factoring. Quadratics which arise from observed measurements and experimental results are more likely to need the use of the quadratic formula for solving. How do you know when to use factoring or quadratic formula? Alan P.